A sign, or representamen, involves a plural relation, for it may be defined as something in which an element of cognition is so embodied as to convey that cognition from the thought of the deliverer of the sign, in which that cognition was embodied, to the thought of the interpreter of the sign, in which that cognition is to be embodied.

1895-6 [c.] | That Categorical and Hypothetical Propositions are one in essence, with some connected matters | CP 1.564

A representation is that character of a thing by virtue of which, for the production of a certain mental effect, it may stand in place of another thing. The thing having this character I term a representamen, the mental effect, or thought, its interpretant, the thing for which it stands, its object.

A Representamen can be considered from three formal points of view, namely, first, as the substance of the representation, or the Vehicle of the Meaning, which is common to the three representamens of the triad, second, as the quasi-agent in the representation, conformity to which makes its Truth, that is, as the Natural Object, and third, as the quasi-patient in the representation, or that which modification in the representation makes its Intelligence, and this may be called the Interpretant. Thus, in looking at a map, the map itself is the Vehicle, the country represented is the Natural Object, and the idea excited in the mind is the Interpretant.

… representation necessarily involves a genuine triad. For it involves a sign, or representamen, of some kind, outward or inward, mediating between an object and an interpreting thought. Now this is neither a matter of fact, since thought is general, nor is it a matter of law, since thought is living.

A sign, or representamen, is something which stands to somebody for something in some respect or capacity. It addresses somebody, that is, creates in the mind of that person an equivalent sign, or perhaps a more developed sign. That sign which it creates I call the interpretant of the first sign. The sign stands for something, its object. It stands for that object, not in all respects, but in reference to a sort of idea, which I have sometimes called the ground of the representamen. “Idea” is here to be understood in a sort of Platonic sense, very familiar in everyday talk; I mean in that sense in which we say that one man catches another man’s idea, in which we say that when a man recalls what he was thinking of at some previous time, he recalls the same idea, and in which when a man continues to think anything, say for a tenth of a second, in so far as the thought continues to agree with itself during that time, that is to have a like content, it is the same idea, and is not at each instant of the interval a new idea.

… I confine the word representation to the operation of a sign or its relation to the object for the interpreter of the representation. The concrete subject that represents I call a sign or a representamen. I use these two words, sign and representamen, differently. By a sign I mean anything which conveys any definite notion of an object in any way, as such conveyers of thought are familiarly known to us. Now I start with this familiar idea and make the best analysis I can of what is essential to a sign, and I define a representamen as being whatever that analysis applies to. If therefore I have committed an error in my analysis, part of what I say about signs will be false. For in that case a sign may not be a representamen. The analysis is certainly true of the representamen, since that is all that word means. Even if my analysis is correct, something may happen to be true of all signs, that is of everything that, antecedently to any analysis, we should be willing to regard as conveying a notion of anything, while there might be something which my analysis describes of which the same thing is not true. In particular, all signs convey notions to human minds; but I know no reason why every representamen should do so.

My definition of a representamen is as follows:

A REPRESENTAMEN is a subject of a triadic relation TO a second, called its OBJECT, FOR a third, called its INTERPRETANT, this triadic relation being such that the REPRESENTAMEN determines its interpretant to stand in the same triadic relation to the same object for some interpretant.

It follows at once that this relation cannot consist in any actual event that ever can have occurred; for in that case there would be another actual event connecting the interpretant to an interpretant of its own of which the same would be true; and thus there would be an endless series of events which could have actually occurred, which is absurd. For the same reason the interpretant cannot be a definite individual object. The relation must therefore consist in a power of the representamen to determine some interpretant to being a representamen of the same object.

1903 | Syllabus: Syllabus of a course of Lectures at the Lowell Institute beginning 1903, Nov. 23. On Some Topics of Logic | EP 2:272-3

A Sign, or Representamen, is a First which stands in such a genuine triadic relation to a Second, called its Object, as to be capable of determining a Third, called its Interpretant, to assume the same triadic relation to its Object in which it stands itself to the same Object. The triadic relation is genuine, that is its three members are bound together by it in a way that does not consist in any complexus of dyadic relations. That is the reason the Interpretant, or Third, cannot stand in a mere dyadic relation to the Object, but must stand in such a relation to it as the Representamen itself does. Nor can the triadic relation in which the Third stands be merely similar to that in which the First stands, for this would make the relation of the Third to the First a degenerate Secondness merely. The Third must indeed stand in such a relation, and thus must be capable of determining a Third of its own; but besides that, it must have a second triadic relation in which the Representamen, or rather the relation thereof to its Object, shall be its own (the Third’s) Object, and must be capable of determining a Third to this relation. All this must equally be true of the Third’s Thirds and so on endlessly; and this, and more, is involved in the familiar idea of a Sign; and as the term Representamen is here used, nothing more is implied. A Sign is a Representamen with a mental Interpretant. Possibly there may be Representamens that are not Signs. Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive power, the sunflower would become a Representamen of the sun. But thought is the chief, if not the only, mode of representation.

1903 | Syllabus: Nomenclature and Division of Triadic Relations, as far as they are determined | EP 2:290-291

In every genuine Triadic Relation, the First Correlate may be regarded as determining the Third Correlate in some respect; and triadic relations may be divided according as that determination of the Third Correlate is to having some quality, or to being in some existential relation to the Second Correlate, or to being in some relation of thought to the Second for something.

A Representamen is the First Correlate of a triadic relation, the Second Correlate being termed its Object, and the possible Third Correlate being termed its Interpretant, by which triadic relation the possible Interpretant is determined to be the First Correlate of the same triadic relation to the same Object, and for some possible Interpretant.

A Sign is a Representamen of which some Interpretant is a cognition of a mind.

I use “sign” in the widest sense of the definition. It is a wonderful case of an almost popular use of a very broad word in almost the exact sense of the scientific definition. [—] I formerly preferred the word representamen. But there was no need of this horrid long word. On the contrary, it requires some stretching to cover such imperative ejaculations of drivers, as “Hi!” or “Hullah”…

Citation

‘Representamen’. Term in M. Bergman & S. Paavola (Eds.), The Commens Dictionary: Peirce's Terms in His Own Words. New Edition. Retrieved from http://www.commens.org/dictionary/term/representamen, 07.12.2016.